Suppose twop perpendicular tangents can be drawn from the origin to the circle x 2 +y 2 -6x-2py+17=0, for some real p. then the value of p=??????
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two perpendicular tangents to a circle is known as director circle.
director circle radius =√2 x given circle
=√2 x√(3^2+p^2-17)
=√(2p^2-16
now center of director circle =(3,p)
now equation of director circle ,
(x-3)^2 +(y-p)^2=(√(2p^2-16))^2
now put x=0 and y=0
(0-3)^2+(0-p)^2=2p^2-16
9+p^2=2p^2-16
p^2=25
p= +_ 5
director circle radius =√2 x given circle
=√2 x√(3^2+p^2-17)
=√(2p^2-16
now center of director circle =(3,p)
now equation of director circle ,
(x-3)^2 +(y-p)^2=(√(2p^2-16))^2
now put x=0 and y=0
(0-3)^2+(0-p)^2=2p^2-16
9+p^2=2p^2-16
p^2=25
p= +_ 5
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